Low-complexity computation of plate eigenmodes with Vekua approximations and the Method of Particular Solutions

This paper extends the Method of Particular Solutions (MPS) to the computation of eigenfrequencies and eigenmodes of plates. Specific approximation schemes are developed, with plane waves (MPS-PW) or Fourier-Bessel functions (MPS-FB). This framework also requires a suitable formulation of the boundary conditions. Numerical tests, on two plates with various boundary conditions, demonstrate that the proposed approach provides competitive results with standard numerical schemes such as the Finite Element Method, at reduced complexity, and with large flexibility in the implementation choices

Blind calibration for compressed sensing by convex optimization

We consider the problem of calibrating a compressed sensing measurement system under the assumption that the decalibration consists in unknown gains on each measure. We focus on {\em blind} calibration, using measures performed on a few unknown (but sparse) signals. A naive formulation of this blind calibration problem, using $\ell_{1}$ minimization, is reminiscent of blind source separation and dictionary learning, which are known to be highly non-convex and riddled with local minima. In the considered context, we show that in fact this formulation can be exactly expressed as a convex optimization problem, and can be solved using off-the-shelf algorithms. Numerical simulations demonstrate the effectiveness of the approach even for highly uncalibrated measures, when a sufficient number of (unknown, but sparse) calibrating signals is provided. We observe that the success/failure of the approach seems to obey sharp phase transitions

Listening to features

This work explores nonparametric methods which aim at synthesizing audio from low-dimensionnal acoustic features typically used in MIR frameworks. Several issues prevent this task to be straightforwardly achieved. Such features are designed for analysis and not for synthesis, thus favoring high-level description over easily inverted acoustic representation. Whereas some previous studies already considered the problem of synthesizing audio from features such as Mel-Frequency Cepstral Coefficients, they mainly relied on the explicit formula used to compute those features in order to inverse them. Here, we instead adopt a simple blind approach, where arbitrary sets of features can be used during synthesis and where reconstruction is exemplar-based. After testing the approach on a speech synthesis from well known features problem, we apply it to the more complex task of inverting songs from the Million Song Dataset. What makes this task harder is twofold. First, that features are irregularly spaced in the temporal domain according to an onset-based segmentation. Second the exact method used to compute these features is unknown, although the features for new audio can be computed using their API as a black-box. In this paper, we detail these difficulties and present a framework to nonetheless attempting such synthesis by concatenating audio samples from a training dataset, whose features have been computed beforehand. Samples are selected at the segment level, in the feature space with a simple nearest neighbor search. Additionnal constraints can then be defined to enhance the synthesis pertinence. Preliminary experiments are presented using RWC and GTZAN audio datasets to synthesize tracks from the Million Song Dataset.Comment: Technical Repor

Robust phase retrieval with the swept approximate message passing (prSAMP) algorithm

In phase retrieval, the goal is to recover a complex signal from the magnitude of its linear measurements. While many well-known algorithms guarantee deterministic recovery of the unknown signal using i.i.d. random measurement matrices, they suffer serious convergence issues some ill-conditioned matrices. As an example, this happens in optical imagers using binary intensity-only spatial light modulators to shape the input wavefront. The problem of ill-conditioned measurement matrices has also been a topic of interest for compressed sensing researchers during the past decade. In this paper, using recent advances in generic compressed sensing, we propose a new phase retrieval algorithm that well-adopts for both Gaussian i.i.d. and binary matrices using both sparse and dense input signals. This algorithm is also robust to the strong noise levels found in some imaging applications

Balancing Sparsity and Rank Constraints in Quadratic Basis Pursuit

We investigate the methods that simultaneously enforce sparsity and low-rank structure in a matrix as often employed for sparse phase retrieval problems or phase calibration problems in compressive sensing. We propose a new approach for analyzing the trade off between the sparsity and low rank constraints in these approaches which not only helps to provide guidelines to adjust the weights between the aforementioned constraints, but also enables new simulation strategies for evaluating performance. We then provide simulation results for phase retrieval and phase calibration cases both to demonstrate the consistency of the proposed method with other approaches and to evaluate the change of performance with different weights for the sparsity and low rank structure constraints

Convex Optimization Approaches for Blind Sensor Calibration using Sparsity

We investigate a compressive sensing framework in which the sensors introduce a distortion to the measurements in the form of unknown gains. We focus on blind calibration, using measures performed on multiple unknown (but sparse) signals and formulate the joint recovery of the gains and the sparse signals as a convex optimization problem. We divide this problem in 3 subproblems with different conditions on the gains, specifially (i) gains with different amplitude and the same phase, (ii) gains with the same amplitude and different phase and (iii) gains with different amplitude and phase. In order to solve the first case, we propose an extension to the basis pursuit optimization which can estimate the unknown gains along with the unknown sparse signals. For the second case, we formulate a quadratic approach that eliminates the unknown phase shifts and retrieves the unknown sparse signals. An alternative form of this approach is also formulated to reduce complexity and memory requirements and provide scalability with respect to the number of input signals. Finally for the third case, we propose a formulation that combines the earlier two approaches to solve the problem. The performance of the proposed algorithms is investigated extensively through numerical simulations, which demonstrates that simultaneous signal recovery and calibration is possible with convex methods when sufficiently many (unknown, but sparse) calibrating signals are provided